Figure 18 shows the progress
of a SA search on the two-dimensional
Rosenbrock function, 
.
Although one would not ordinarily choose to
use SA on a problem which is amenable to solution by more efficient
methods, it is interesting to do so for purposes of comparison. Each
of the solutions accepted in a 1000 trial search is shown (marked by
symbols). The algorithm employed the adaptive step size selection
scheme of equations (67) and (68).
It is apparent that the search is
wide-ranging but ultimately concentrates in the neighborhood of the
optimum.
Figure 18: Minimization of the Two-dimensional Rosenbrock Function by Simulated Annealing --- Search Pattern.
Figure 19 shows the progress in reducing the objective function for the same search. Initially, when the annealing temperature is high, some large increases in f are accepted and some areas far from the optimum are explored. As execution continues and T falls, fewer uphill excursions are tolerated (and those that are tolerated are of smaller magnitude). The last 40% of the run is spent searching around the optimum. This performance is typical of the SA algorithm.
